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Supplementum defectus geometria Cartesianae circa inventionem locorum. + Curvatura radii in diaphanis non uniformibus. + [Five other papers on the Brachistochrone problem contained in the 'Acta Eruditorum' of 1696 and 1697].


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Leipzig: Gross & Fritsch, 1696-97. 4to. (201x169mm). (2),606;(8),594 pp. and 17 engraved folding plates (complete). Double-volume of the Acta Eruditorum for the years 1696 and 1697. An exceptionally fine and clean copy in contemporary vellum. In the June issue of Acta Eruditorum for the year 1696 Johann Bernoulli published a paper in which he presented a challenge to the best mathematicians:"Let two points A and B be given in a vertical plane. To find the curve that a point M, moving on a path AMB , must follow such that, starting from A, it reaches B in the shortest time under its own gravity."Johann adds that this curve is not a straight line, but a curve well known to geometers, and that he will indicate that curve, if nobody would do so that year. Later that year Johann corresponded directly with Leibniz regarding his challenge. Leibniz solved the problem the same day he received notice of it, and almost correctly predicted a total of only five solutions: from the two Bernoullis, himself, L’Hospital, and Newton. Leibniz was convinced that the problem could only be solved by a mathematician who mastered the new field of calculus. (Galileo had formulated and given an incorrect solution to the problem in his Dialogo). But by the end of the year Johann had still not received any other solutions. However, Leibniz convinced Johann that he should extend the deadline to Easter and that he should republish the problem. Johann now had copies of the problem sent to Journal des sçavans, the Philosophical Transactions, and directly to Newton. Earlier that year Johann had accused Newton for having filched from Leibniz’ papers. Manifestly, both Johann and Leibniz interpreted the silence from June to December as a demonstration that the problem had baffled Newton. They intended now to demonstrate their superiority publicly. But Newton sent a letter dated Jan. 30 1697 to Charles Montague, then president of the Royal Society, in which he gave his solution and mentioned that he had solved it the same day that he received it. Montague had Newton’s solution published anonymously in the Philosophical Transactions. However, when Bernoulli saw this solution he realized from the authority which it displayed that it could only have come from Newton (Bernoulli later remarked that he 'recognized the lion by its claw'). During the fall of 1697 Bernoulli further received solutions from his brother Jakob, L’Hospital, and Tschirnhaus. In the May issue of Acta Eruditorum Bernoulli published these different solutions together with his own, and revealed to the learned world that the sought curve, which he called a brachistochrone, is a cycloid. Among the solutions the two by the Bernoulli brothers were of particular importance. Johann had ingeniously reformulated the challenge as a problem belonging to optics, i.e., the bending of a light ray through a transparent nonuniform media, and applied Fermat’s principle of least time. He thus demonstrated the fundamental parallel between geometric optics and point mechanics, which would lead to the work of W.R. Hamilton in the 1830’s. The solution by Jokab also contains a general principle, namely, that a curve which constitutes a maximum or minimum as a whole must also possess this property in the infinitesimal - the fundamental principle of the calculus of variations. N° de ref. de la librería 38034

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Título: Supplementum defectus geometria Cartesianae ...

Encuadernación: Soft cover

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Herman H. J. Lynge & Søn A/S was founded in 1821 and is the oldest antiquarian bookseller in Scandinavia. We specialize mainly in important and rare books in all fields of Science and the Humanities.

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